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arXiv:1909.01099 · Acta Physica Polonica B

Modelling the Inverse Zeno Effect for the Neutron Decay

Francesco Giacosa

Published Dec 19, 2019• 0 citations
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Abstract

Beam and trap methods find incompatible results for the lifetime of the neutron: the former delivers a value which is about $8.7\pm2.1$ s longer than the latter. Very recently (1906.10024) it has been proposed that the inverse Zeno effect (IZE) could be responsible for the shorter lifetime in trap experiments. Here, we compare two different models of measurement, one obtained by bang-bang measurements and by a continuous measurement: the IZE turns out to be in both cases very similar, showing that the results do not depend on the details of the measurement process.

DOI
10.5506/aphyspolb.51.77

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Beam and trap methods find incompatible results for the lifetime of the neutron: the former delivers a value which is about 8.7±2.18.7\pm2.18.7±2.1 s longer than the latter. Very recently (1906.10024) it has been proposed that the inverse Zeno effect (IZE) could be responsible for the shorter lifetime in trap experiments. Here, we compare two different models of measurement, one obtained by bang-bang measurements and by a continuous measurement: the IZE turns out to be in both cases very similar, showing that the results do not depend on the details of the measurement process.
The lifetime of the neutron, although being a fundamental quantity in particle physics, is to date still associated with a puzzle: different techniques of measurements find values of the lifetime which are mutually incompatible. While methods based on beams of neutrons find a (average) value τnbeam=888.1±2.0\tau_{n}^{\text{beam}} =888.1\pm2.0τnbeam​=888.1±2.0 s, methods based on traps obtain a shorter lifetime τntrap=879.37±0.58\tau_{n} ^{\text{trap}}=879.37\pm0.58τntrap​=879.37±0.58 s, i.e. a ∼4σ\sim 4\sigma∼4σ mismatch. This is the so-called neutron decay anomaly. We propose here a novel interpretation of this puzzle based solely on quantum mechanics (no need of physics beyond the standard model): if the measurement apparatus and the surrounding environment are able to observe the unstable system at very short (but not too short) times after the preparation of it, the so called inverse quantum Zeno (IZE) effect can take place: the IZE corresponds an increase of the decay rate through the interaction of the system with the environment. We argue that such a quantum phenomenon can be realized in the case of trap experiments but not in the case of beam experiments. There are mainly two reasons behind our interpretation of the neutron decay anomaly: (i) the intrinsic dependence of the 3-body weak decay rate on the Q value of the decay (the Sargent rule); (ii) the very peculiar setup of neutron traps, in which up to ∼108\sim 10^{8}∼108 ultra cold neutrons are confined together. This feature can help to increase the frequency of dephasing of the wave function (equivalent to the `collapse'), necessary to obtain the inverse quantum Zeno effect.
We discuss a simple and analytically solvable measurement model which describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE), that correspond to the slow down and to the increase of the decay rate caused by measurements (or, more in general, by the interaction of an unstable state with the detector and the environment). Within this model one can understand quite general features of the QZE and IZE: by considering an unstable quantum state, such as an unstable particle, whose decay width as function of energy is Γ(ω)=g2ωα,Γ(ω)=g^{2}ω^α,Γ(ω)=g2ωα, then -- under quite general assumptions -- the QZE occurs for α∈(0,1)α\in(0,1)α∈(0,1), while the IZE for α∈(−∞,0)∪(1,∞).α\in(-\infty,0)\cup(1,\infty).α∈(−∞,0)∪(1,∞). This result is valid also for more realistic measurement models than the one described in this work. We then apply these considerations to the decay of the neutron, for which α=5.α=5.α=5. Hence, the realization of the IZE for the neutron decay (and for the majority of weak decays) is in principle possible. Indeed, trap experiments find a lifetime that is 8.7±2.18.7\pm2.18.7±2.1 s shorter than beam experiments, suggesting that the IZE could have taken place.
Quantum mechanics predicts that the decay rate of unstable systems could be effectively modified by the process of the measurement of the survival probability. Depending on the intrinsic properties of the unstable system and the experimental setup for the observation, one could obtain the so called (direct) quantum Zeno and inverse quantum Zeno effects corresponding to a slowing down or a speeding up of the decay, respectively. We argue that the inverse quantum Zeno effect is in principle detectable at a percent level for the neutron decay in experiments with trapped ultracold neutrons. Conversely, this effect is basically undetectable in experiments in which the neutron lifetime is measured by measuring the decays of beams of neutrons. As a test of our claim, we propose a simple qualitative correlation between the number of neutrons in the trap and the neutron lifetime: the larger the number, the faster the decay. Finally we discuss also the presently available measurements of the neutron lifetime and address the issue of the possible discrepancy that has been reported among the results obtained by the different experimental techniques.
It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.
After reviewing the description of an unstable state in the framework of nonrelativistic Quantum Mechanics (QM) and relativistic Quantum Field Theory (QFT), we consider the effect of pulsed, ideal measurements repeated at equal time intervals on the lifetime of an unstable system. In particular, we investigate the case in which the ‘bare’ survival probability is an exact exponential (a very good approximation in both QM and QFT), but the measurement apparatus can detect the decay products only in a certain energy range. We show that the Quantum Zeno Effect can occur in this framework as well.